1. Field
The present invention relates to a detection and ranging device and detection and ranging method with a transmission sensor array and a reception sensor array that is formed of n (2≦n) sensor elements, estimating a target count indicating the number of targets based on reflected signals of transmission signals sent from the transmission sensor array and reflected from the targets, and estimating an angle at which each reflected signal comes based on the target count.
2. Description of the Related Art
Conventionally, in a detection and ranging device having a sensor array formed of a plurality of sensor elements as a reception antenna to detect the target count and the position of each target based on reflected waves of transmission waves coming from a transmission sensor array and reflected from the targets, it is important in device performance how accurately the number of reflected waves and their coming directions can be detected.
For example, as depicted in FIG. 7, it is assumed that, to a uniformly spaced linear array antenna (hereinafter, START Uniform Linear Array (ULA)) formed of n sensor elements (sensor elements 106a1 to 106an) arranged on an X axis so that a distance between adjacent sensor elements is d, independent echo signals reflected from m targets β (reflection of transmission waves) are incident at each different angle θβ (an angle measured with the position of the sensor element 106a1 being taken as a coordinate origin, the normal to the X axis being taken as an Y axis, and further a clockwise direction with reference to a positive direction of the Y axis (arrow direction of the Y axis) being taken as a positive direction of the angle), where β is a target number with β=1, 2, . . . , m.
Here, a signal vα(t) obtained by demodulating the signal received by an α-th (α=1, 2, . . . , n) sensor element at a time t can be represented by the following equation, where the first sensor element 106a1 is taken as a phase reference, xβ(t) is a baseband signal, and nα(t) is an additive Gaussian noise signal of power σ:
                                          v            α                    ⁡                      (            t            )                          =                                            ∑                              β                =                1                            m                        ⁢                                                            x                  β                                ⁡                                  (                  t                  )                                            ⁢                              exp                ⁡                                  (                                      j                    ⁢                                                                                  ⁢                                          ϕ                                              α                        ,                        β                                                                              )                                                              +                                                    n                α                            ⁡                              (                t                )                                      ⁢                          (                                                α                  =                  1                                ,                2                ,                …                ⁢                                                                  ,                n                            )                                                          (        1        )            
In Equation 1, “exp” is an exponential function with natural logarithm in base, and j is an imaginary unit. Also, φα,β is defined in the following equation, where λ is a wavelength of a carrier signal of a transmission wave:
                              ϕ                      α            ,            β                          ≡                                            2              ⁢              Π                        λ                    ⁢                      (                          α              -              1                        )                    ⁢          d          ⁢                                          ⁢          sin          ⁢                                          ⁢                      θ            β                                              (        2        )            
Then, Equation 1 for all α can be represented with a vector V(t) as in the following equation:
                              V          ⁡                      (            t            )                          =                              [                                                                                                                              ∑                                                  β                          =                          1                                                m                                            ⁢                                                                                                    x                            β                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  exp                          ⁡                                                      (                                                          jφ                                                              1                                ,                                β                                                                                      )                                                                                                                +                                                                  n                        1                                            ⁡                                              (                        t                        )                                                                                                                                          ⋰                                                                                                                                                ∑                                                  β                          =                          1                                                m                                            ⁢                                                                                                    x                            β                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  exp                          ⁡                                                      (                                                          jφ                                                              n                                ,                                β                                                                                      )                                                                                                                +                                                                  n                        n                                            ⁡                                              (                        t                        )                                                                                                                  ]                    =                                    AX              ⁡                              (                t                )                                      +                          N              ⁡                              (                t                )                                                                        (        3        )            
Here, an angular vector (mode vector) a(θβ) is defined by the following equation:
                              a          ⁡                      (                          θ              β                        )                          ≡                              [                                                                                exp                    ⁡                                          (                                              jϕ                                                  1                          ,                          β                                                                    )                                                                                                                    ⋰                                                                                                  exp                    ⁡                                          (                                              jϕ                                                  n                          ,                          β                                                                    )                                                                                            ]                    ⁢                      (                                          β                =                1                            ,              2              ,              …              ⁢                                                          ,              m                        )                                              (        4        )            
A matrix A, a vector X(t), and a vector N(t) in Equation 3 are defined as in the following equations:
                              A          ≡                      [                                          a                ⁡                                  (                                      θ                    1                                    )                                            ⁢                                                          ⁢              …              ⁢                                                          ⁢                              a                ⁡                                  (                                      θ                    m                                    )                                                      ]                          =                  [                                                                      exp                  ⁡                                      (                                          jϕ                                              1                        ,                        1                                                              )                                                                              …                                                              exp                  ⁡                                      (                                          jϕ                                              1                        ,                        m                                                              )                                                                                                      ⋰                                                                                                                          ⋰                                                                                      exp                  ⁡                                      (                                          jϕ                                              n                        ,                        1                                                              )                                                                              …                                                              exp                  ⁡                                      (                                          jϕ                                              n                        ,                        m                                                              )                                                                                ]                                    (        5        )                                          x          ⁡                      (            t            )                          ≡                              [                                                            x                  1                                ⁡                                  (                  t                  )                                            ,              …              ⁢                                                          ,                                                x                  m                                ⁡                                  (                  t                  )                                                      ]                    T                                    (        6        )                                          N          ⁡                      (            t            )                          ≡                              [                                                            n                  1                                ⁡                                  (                  t                  )                                            ,              …              ⁢                                                          ,                                                n                  n                                ⁡                                  (                  t                  )                                                      ]                    T                                    (        7        )            
Note that a superscript “T” appearing in “[x1(t), . . . , xm(t)]T” in Equation 6 and “[n1(t), . . . , nn(t)]T” in Equation 7 represents a transpose of a vector or matrix.
When a covariance matrix Rvv of V(t) is calculated from Equation 3 assuming that X(t) and N(t) are not correlated with each other, Equation 8 below holds, where “I” in Equation 8 represents a unit matrix and σ is power of the noise signal as explained above:Rvv≡E[V(t)VH(t)]=ARxxAH+σ2I  (8)
Rvv represented in Equation 8 is a generic operand when angle estimation of the target is performed. Here, a superscript “H” attached as “VH(t)” and “AH” represents a Hermitian conjugate of a vector or matrix. Rxx is a covariance matrix of the baseband signals, and is defined by the following equation:Rxx≡E[X(t)XH(t)]  (9)
Here, since the echo signal received by the ULA is none other than a transmission signal generated from the identical signal source and reflected from the target, the Rank of the n-order matrix Rvv reduces to 1. Therefore, if calculations, such as an inverse-matrix operation and eigenvalue decomposition, were tried on to the original covariance matrix Rvv, they may not be able to be performed.
To solve this problem, a scheme of taking (n−L+1) L-order square submatrixes in a main diagonal direction of Rvv and adding them together for averaging (Forward Spatial Smoothing (FSS)), a scheme of reversing the reference point of the ULA to perform a similar operation (Backward Spatial Smoothing (BSS)), or a combination thereof (FBSS) is conventionally used.
For example, in MUltiple SIgnal Classification (MUSIC), an L-order square matrix RvvFBSS obtained in this manner is first subjected to eigenvalue decomposition as in the following equation to find a matrix EN formed of eigenvectors corresponding to a noise eigenvalue:RVVFBSS=EΛEH(=ESΛSESH+σ2ENENH)  (10)
In Equation 10, Λ, ΛS, and E are as follows, where ΛS is a matrix formed of an eigenvalue λβ (β=1, 2, . . . , m) of the reflected signal (target echo), ES is a matrix formed of eigenvectors (E1 to Em, sometimes referred as signal-eigenvectors) which span signal-subspace, σ2IL is a L-order unit matrix multiplied by noise power σ2, and EN is a matrix formed of eigenvectors (Em+1 to EL, sometimes referred as noise-eigenvectors) which span over a noise-subspace, and where “diag[λ1, . . . , λm]” appearing in Equation 12 for ΛS represents a diagonal matrix having diagonal elements of λ1, . . . , λm:
                    Λ        =                              [                                                                                Λ                    S                                                                    0                                                                              0                                                                      0                                          L                      -                      m                                                                                            ]                    +                                    σ              2                        ⁢                          I              L                                                          (        11        )                                          Λ          S                =                  diag          ⁡                      [                                          λ                1                            ,              …              ⁢                                                          ,                              λ                m                                      ]                                              (        12        )                                E        ≡                  [                                    E              S                        ❘                          E              N                                ]                ≡                  [                                                    E                1                            ⁢                                                          ⁢              …              ⁢                                                          ⁢                              E                m                                      ❘                                          E                                  m                  +                  1                                            ⁢                                                          ⁢              …              ⁢                                                          ⁢                              E                L                                              ]                                    (        13        )            
Then, the angle θβ of the target β is estimated with Equation 14 below. That is, by using the angular vector a(θ) defined by Equation 4 with θ as a parameter, angular information included in the L-order square matrix RvvFBSS is scanned to find an angle when a peak appears in Pmusic(θ), thereby performing angle estimation for each target β (β=1, 2, . . . , m)
                                          P            music                    ⁡                      (            θ            )                          =                                                            a                H                            ⁡                              (                θ                )                                      ⁢                          a              ⁡                              (                θ                )                                                                                        a                H                            ⁡                              (                θ                )                                      ⁢                          E              N                        ⁢                          E              N              H                        ⁢                          a              ⁡                              (                θ                )                                                                        (        14        )            
To correctly perform angle estimation, it is required to select a submatrix of an appropriate size L (in FBSS, L≧m+1 and n−L+1≧m) according to target count m, and by applying spatial average to recover the Rank of Rvv to find EN of a correct size.
However, in general, the target count m is unknown. Therefore, conventionally, an arbitrary L is set to find RvvFBSS, an eigenvalue of a diagonal element of that matrix Λ is found, and then, for example, a statistical index Akaike's Information Criterion (AIC)(i) defined by Equation 15 below is introduced, thereby estimating the feasible target count, where ND in Equation 15 represents the number of data samples:
                              A          ⁢                                          ⁢          I          ⁢                                          ⁢                      C            ⁡                          (              i              )                                      ≡                                            -                                                N                  D                                ⁡                                  (                                      L                    -                    i                                    )                                                      ⁢            log            ⁢                          {                                                                                          (                                                                        ∏                                                      j                            =                                                          i                              +                              1                                                                                L                                                ⁢                                                  λ                          j                                                                    )                                                              l                                              L                        -                        i                                                                              /                                      l                                          L                      -                      i                                                                      ⁢                                                      ∑                                          j                      =                                              i                        +                        1                                                              L                                    ⁢                                      λ                    j                                                              }                                +                      ⅈ            ⁡                          (                                                2                  ⁢                  L                                -                i                            )                                                          (        15        )            
A value p of a parameter i (natural number) that gives a minimum value in Equation 15 is assumed to show the reasonable target count and is parametrically found by Equation 16 below, where “arg min[AIC(i)]” in Equation 16 represents an operation of scanning the parameter i to find a minimum value of “AIC(i)” by:
                    p        =                              argmin            i                    ⁡                      [                          A              ⁢                                                          ⁢              I              ⁢                                                          ⁢                              C                ⁡                                  (                  i                  )                                                      ]                                              (        16        )            
As a matter of course, relevance of the result of Equation 16 cannot be ensured unless estimation of Λ is relevant. Therefore, the value “L” in Equation 15 has to be variously changed within an allowable range to try calculations by Equation 16. This requires a large amount of calculation even only for eigenvalue decomposition by Equation 10, thereby increasing the processing time and further increasing the calculation load.
Furthermore, as is evident from Equation 11, to the diagonal element of Λ, a noise component is always superposed even to a signal-component portion. Therefore, in particular, for the use in an environment where a Signal to Noise Ratio (SNR) (hereinafter, S/N ratio) is poor, such as in a vehicle-mounted radar, reliability of target-count estimation is extremely low.
Moreover, in a detection and ranging device achieving a target angle estimating function by using a sensor array, it is often the case that an algorithm that necessitates correct estimation of the target count is adopted as a preprocess for angle estimation. However, to compensate coherency of a probe signal (transmission signal from the device) by spatial average and recover the Rank of the signal covariance matrix to achieve successful estimation of the target count, the target count has to be correctly estimated, posing a recursive algorithm-structure problem.
For this reason, a calculation by applying spatial average by using a submatrix with its size arbitrarily taken as a kind of parameter to find an eigenvalue of the obtained spatial average matrix for evaluation with a statistical index, such as AIC, has to be performed by trial and error, while the size of the submatrix is being changed by turns.
Still further, calculation for eigenvalue decomposition of an n-order matrix requires an amount of calculation on the order of 4n3, for example. Since this calculation is performed parametrically in target-count estimation, an approximately ten-fold amount of calculation is further required. For this reason, it is difficult to achieve applications to vehicle-mounted radars with low central processing units (CPU) performance and mobile devices requiring rapid updates of detection and ranging information. Still further, to all diagonal elements of the diagonal matrix obtained through eigenvalue decomposition on a normal signal covariance matrix, noise power is added, which makes estimation extremely vulnerable to deterioration in S/N ratio.
For this reason, to ensure reliability of angle estimation, as disclosed in Japanese Patent Application Laid-open No. 2005-181168, for example, a wave-number estimating device is suggested that generates a covariance matrix E[XXH]=Rxx of a time-domain data vector X, performs Fast Fourier Transform (FFT) on the time-domain data vector X to clip a signal equal to or smaller than an appropriate threshold, performs Inverse Fast Fourier Transform (IFFT) to generate a white data vector Y (in other words, data Y is obtained by applying the white-noise method to data X), performs Cholesky decomposition on a covariance matrix of the data vector Y with E[YYH]=LLH to generate a matrix R=L−1RxxL−H in which correlation waves were suppressed, and then performs eigenvalue decomposition on R, thereby increasing accuracy of AIC.
Also, to reduce the amount of calculation for angle estimation, as disclosed in Japanese Patent Application Laid-open No. 2002-243826, for example, an electromagnetic-wave incoming-direction estimating device is suggested that generates a covariance matrix E[XXH]=Rxx of a data vector X, performs eigenvalue decomposition with Rxx=ESΛSESH+σ2ENENH, performs Cholesky decomposition on a matrix formed of noise eigenvectors with ENENH=LLH, and then calculates an angular spectrum P(θ)=aH(θ)a(θ)/|LHa(θ)|2 (where a(θ) represents an angular vector (mode vector) with θ as a parameter) by using as a lower triangular matrix, thereby reducing the calculation load of angle estimation and the like.
Furthermore, as disclosed in International Patent Publication No. 2006/67869, for example, an incoming-wave estimating device is suggested that generates, when estimating the number of incoming waves received by an array antenna, a correlation matrix based on array covariance matrixes based on the incoming waves, generates an estimation matrix for estimating the number of incoming waves by using this correlation matrix, performs QR decomposition on this estimation matrix, and then estimates the number of incoming waves based on the elements on each row of an upper triangular matrix as a result of QR decomposition, thereby estimating the number of incoming waves without performing eigenvalue decomposition with a large calculation load.
However, in the conventional technology typified by Japanese Patent Application Laid-open No. 2005-181168 and Japanese Patent Application Laid-open No. 2002-243826, in the case of an n-order matrix, the amount of calculation required for eigenvalue decomposition is on the order of 8n3/3 to 4n3. Furthermore, when even eigenvectors are also to be stored, an amount of calculation on the order of 20n3 at minimum is required, thereby increasing the processing load.
In the conventional technology typified by Japanese Patent Application Laid-open No. 2002-243826, relevance of the result of angle estimation cannot be ensured unless estimation of the target count m is correct. Therefore, it is required to variously change the size L of the submatrix for use in calculation of a spatial average matrix within an allowable range to try target-count estimation many times. That is, time is required not only for eigenvalue calculation itself but also for trial and error process, requiring an enormous amount of calculation, but it is not always the case that an appropriate result of angle estimation can be obtained in return for the increased computation load.
Furthermore, in the conventional technology typified by International Patent Publication No. 2006/67869, by using an index based on the elements of the upper triangular matrix R as a result of QR decomposition on a pseudo covariance matrix in which a noise influence is extremely low, the target count can be estimated more quickly and accurately. However, although in this technology, the pseudo covariance matrix is decomposed into an orthogonal matrix Q and an upper triangular matrix R which diagonal elements are eigenvalues of the pseudo covariance matrix, the amount of calculation required is on the order of 4n3/3 in the case of an n-order matrix, which is still large in view of the calculation load. Therefore, it is difficult to apply the conventional technology to low-performance CPUs or mobile terminals.